Answer:
a. 200 received in 5 years is the most valuable, $300 received in 10 years is the second most valuable, while $100 received in one year is the least valuable.
b. $300 received in 10 years is the most valuable, $200 received in 5 years is the second most valuable, while $100 received in one year is the least valuable.
c. $100 received in one year is the most valuable, $200 received in 5 years is the second most valuable, while $300 received in 10 years is the least valuable.
Step-by-step explanation:
Note: This question is not complete. The complete question is therefore provided before answering the question as follows:
Consider the following alternatives:
i. $100 received in one year
ii. $200 received in 5 years
iii. $300 received in 10 years
a. Rank the alternatives from most valuable to least valuable if the interest rate is 10% per year.
b. What is your ranking if the interest rate is only 5% per year?
c. What is your ranking if the interest rate is 20% per year?
The explanation of the answers is now given as follows:
The ranking can be done after calculating the present value of each amount using the following present value (PV):
PV = FV / (1 + r)^n ………………… (1)
Where;
PV = Present value of the amount
FV = Future value of the amount or the amount to be received
r = interest rate
n = number of years
Ranking rule: After applying the above PV formula, the largest PV is ranked as the most valuable while the lowest PV is ranked as the least valuable.
Therefore, we can now proceed as follows:
a. Rank the alternatives from most valuable to least valuable if the interest rate is 10% per year.
Using equation (1), we have:
i. PV of $100 received in one year = $100 / (1 + 10%)^1 = $90.91
ii. PV of $200 received in 5 years = $200 / (1 + 10%)^5 = $124.18
iii. PV of $300 received in 10 years = $300 / (1 + 10%)^10 = $115.66
Based on the calculated PVs and the ranking rule above, $200 received in 5 years is the most valuable, $300 received in 10 years is the second most valuable, while $100 received in one year is the least valuable.
b. What is your ranking if the interest rate is only 5% per year?
Using equation (1), we have:
i. PV of $100 received in one year = $100 / (1 + 5%)^1 = $95.24
ii. PV of $200 received in 5 years = $200 / (1 + 5%)^5 = $156.71
iii. PV of $300 received in 10 years = $300 / (1 + 5%)^10 = $184.17
Based on the calculated PVs and the ranking rule above, $300 received in 10 years is the most valuable, $200 received in 5 years is the second most valuable, while $100 received in one year is the least valuable.
c. What is your ranking if the interest rate is 20% per year?
Using equation (1), we have:
i. PV of $100 received in one year = $100 / (1 + 20%)^1 = $83.33
ii. PV of $200 received in 5 years = $200 / (1 + 20%)^5 = $80.38
iii. PV of $300 received in 10 years = $300 / (1 + 20%)^10 = $48.45
Based on the calculated PVs and the ranking rule above, $100 received in one year is the most valuable, $200 received in 5 years is the second most valuable, while $300 received in 10 years is the least valuable.